Algebraic theory of identification in parametric models

Abstract

The article presents the problem of identification in parametric models from an algebraic point of view. We argue that it is not just another perspective but the proper one. That is, using our approach we can see the very nature of the identification problem, which is slightly different than that suggested in the literature. In practice, it means that in many models we can unambiguously estimate parameters that have been thought as unidentifiable. This is illustrated in the case of Simultaneous Equations Model (SEM), where our analysis leads to conclusion that existing identification conditions, although correct, are based on the inappropriate premise: only the structural parameters that are in one–to–one correspondence with the reduced form parameters are identified. We will show that this is not true. In fact, there are other structural parameters, which are identified, but can not be uniquely recovered from the reduced form parameters. Although we apply our theory only to SEM, it can be used in many standard econometric models.

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